Consider the arrangment shown that is at rest. Each pulley has mass m and radius R. (a) If we release the system, with what speed does the 3m mass hit the spring (which was a distance h below its intial position)? (b) If the spring undergoes a maximum compression of h, what is the spring constant k? (c) Does the maximum compression of the spring depend on whether or not the pulleys had mass?
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- A star of radius R = 2.3 * 108m rotates with an angular speed v = 2.4 * 10-6rad>s. Ifthis star collapses to a radius of 20.0 km, find its final angular speed. (Treat the star as if itwere a uniform sphere, and assume that no mass is lost as the star collapses.)Hello, it gives that my answer is wrong and I don’t know why its wrong. Any help?S r WO If the ring, of weight 8-lb and radius 2- in, rolls without slipping on a distance 47-in, determine the work of the gravitational force. The slope forms an angle 13* with the horizontal.
- Needs Complete solution with 100 % accuracy don't use chat gpt or ai plz plz plz plz.R R A mass m = 88 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.8 m and finally a flat straight section at the same height as the center of the loop (15.8 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) 1) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s Submit 2) What height above the ground must the mass begin to make it around the loop-the-loop? m Submit 3) If the mass has just enough speed to make around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s Submit +In the figure below, a solid brass ball of mass m will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular motion has radius R, and the ball has radius r << R. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.) (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? 27R 10 h = (b) If the ball is released at height = 6R, what is the magnitude of the horizontal force component acting on the ball at point Q? 50mg 7 F =
- A uniform sphere of mass m and radius R rolls without slipping down a plane at an angle θ from thehorizontal. Show that the acceleration along the slope of the center of mass is aCM = (5/7)g sin θ and that the force of static friction needed is fs = (2/7)mg sin θ. What minimum coefcient of friction µs is needed to satisfythe conditions of the problem?A painter (of mass 75 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 72 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building. If the bars are separated by a distance 2.6 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall? d =Show that y'(x) = 0 only at x = 0, and thus that it fol- lows (why?) that the maximum deflection of the cantilever is ymax = y(L) = wL^/(8EI).
- show workA winch with a drum of radius R pulls a block at constant speed up a rough incline. The winch is attached to the block with a lightweight, thin cable that runs over a massless roller pulley that turns without friction, as shown. The mass of the block is M, the coefficient of kinetic friction between the block and the incline is μ, and the angle of the incline is 0. Let g denote the acceleration due to gravity. Derive an algberaic expression for the power P supplied by the winch if the winch turns through a total angular displacement during a time interval At. P =The scientist Archimedes is famed to have once said “Give me a lever long enough and I’ll move the world”. Let us assume that Archimedes is approximately (60 kg) and the world has a mass of approximately (6×1024kg). If the fulcrum of our lever is (1 m) away from the Earth’s side, how long is our lever? (Assume that all of this takes place on an infinite plane with Earth surface gravity.) (Give your answer in units of the distance to the galaxy Andromeda which is 770 kpc away. You will need to convert from meters.)